Cremona's table of elliptic curves

5082 = 2 · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	5082s	Isogeny class
Conductor	5082	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	9817285632 = 210 · 3 · 74 · 113	Discriminant
Eigenvalues	2- 3+  0 7- 11+ -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1768,-28951]	[a1,a2,a3,a4,a6]
Generators	[-23:25:1]	Generators of the group modulo torsion
j	459206250875/7375872	j-invariant
L	4.9514548751978	L(r)(E,1)/r!
Ω	0.73697130086733	Real period
R	0.33593267942527	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40656bz1 15246n1 127050ci1 35574cp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082s1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	0	-	+	-2	2	-2	-2	-10	-4	-2	-2	6	-10	12	4	-2	-12	2	-4	4	-8	-6	6

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Quadratic twists for elliptic curve 5082s1

-4	-3	5	-7	-11
40656bz1	15246n1	127050ci1	35574cp1	5082a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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